基于测度迁移的非齐次Poisson过程强度建模与估计
Non-Homogeneous Poisson Process Intensity Modeling and Estimation using Measure Transport
摘要：
非齐次泊松过程被广泛应用于从环境科学到健康科学的科学领域。通常，点过程中感兴趣的中心对象是潜在的强度函数。在这里，我们提出了一个一般模型的强度函数的非齐次泊松过程使用测量运输。该模型是从一个灵活的双射映射建立的，该映射从感兴趣的底层强度函数映射到一个更简单的参考强度函数。我们执行双射性建模的地图作为一个组成的多个简单的双射映射，并表明该模型具有重要的近似属性。灵活映射的估计在优化框架内完成，其中使用深度学习和图形处理单元中的最新技术进步来高效地完成计算。虽然我们发现，用我们的方法得到的强度函数估计不一定优于使用传统方法得到的，建模表示带来了它的其他优点，如方便点过程模拟和不确定性量化。在更高的维度建模点过程也有利于使用我们的方法。我们说明了使用我们的模型对模拟数据，和一个真实的数据集，包含自1964年以来斐济附近的地震事件的位置。
英文摘要：
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity function. Here, we present a general model for the intensity function of a non-homogeneous Poisson process using measure transport. The model is built from a flexible bijective mapping that maps from the underlying intensity function of interest to a simpler reference intensity function. We enforce bijectivity by modeling the map as a composition of multiple simple bijective maps, and show that the model exhibits an important approximation property. Estimation of the flexible mapping is accomplished within an optimization framework, wherein computations are efficiently done using recent technological advances in deep learning and a graphics processing unit. Although we find that intensity function estimates obtained with our method are not necessarily superior to those obtained using conventional methods, the modeling representation brings with it other advantages such as facilitated point process simulation and uncertainty quantification. Modeling point processes in higher dimensions is also facilitated using our approach. We illustrate the use of our model on both simulated data, and a real data set containing the locations of seismic events near Fiji since 1964.
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